If the battery is dying quickly, you might have a short in the system somewhere that is eating the battery when it is just sitting there. Do you have a multimeter or some way to check voltage on the battery, and check to see if there is a drain on the battery when the car is shut off? Some things, like the clock and any alarm system will draw a little current, but you are seeing some significant current draw to kill a new battery in a day.
Did the old battery work ok for a few months and then die, followed by a new battery dying in a matter of hours? Was the new battery fully charged before it died?
Have you checked the connections to the alternator? There is a plug that is held in by a spring clip and a small wire that connects to a screw on the body of the alternator. If these have worked loose, it is not likely that the battery would be ok after a few starting episodes, as the alternator may not charge at all depending on which wires might not be connected properly.
Also, a bad ground would interfere with charging and possibly contribute to the symptoms you have experienced. The ground for the battery is on the inner fender on the passenger side, easily traced from the negative pole of the battery. Unscrew the bolt to the fender and clean any corrosion on the bolt, the fender and connector, then put it back together.
Hope this helps; if you have any more information please post it so others can add to the list of potential solutions. Good luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)